https://play.google.com/store/apps/details?id=com.ssbcrackexams.learn

100 math’s formulas, tips and trick for AFCAT exam

The math’s curriculum of AFCAT is basically 8 topics of quantitative aptitude. These topics with highest weightage to lowest weightage of questions in AFCAT Numerical Ability Section which includes around 18 questions are;

1. Speed, Distance and Time 2. Work and Time 3. Percentage 4. Average 5. Simple and Compound interest 6. Ratio & Proportion 7. Profit & Loss. 8. Decimal Fraction/ Simplification

In AFCAT exam mathematics is the subject from where you can score 100%. Though questions

in Numerical Ability Section are based on simple 10th level arithmetic, what one needs to be

good with are the Important Formulas, Simple tricks and tips, Accurate calculation-based

approach and finally Improves one’s speed of doing the questions which are interconnected

and dependent as a cycle of shortcut bunch of Best confidence to have in one’s to appear for

any question in Numerical Ability Section of your AFCAT 2020 exam paper.

This article gives you clear idea about all those important formulas on each topic in

Numerical ability syllabus as mentioned above starting with highest weightage topic to

lowest weightage topic.

Shortcut formulas

Simple tricks and

Tips

Accurate calculation approach

Speed of doing the questions

1. Speed, Distance and Time (SDT)

Speed: The distance travelled by any object or a person per unit time is known as

speed of that object or a person.

Distance: The length of the path travelled by any object or a person or a vehicle

between two places is known as ‘Distance’.

Time: The duration in hours, minutes or seconds spent to cover distance is called

‘Time’.

Conversion of unit: (Most frequently used shortcut in problem solving on SDT topic)

➢ To convert speed of an object from km/h to m/s, multiply it by 𝟓

𝟏𝟖.

➢ To convert speed of an object from m/s to km/h, multiply it by 𝟏𝟖

𝟓

Average Speed: The average speed of an object is defined as total distance travelled

divided by total time taken. Shortcut formula

Relative Speed: The speed of an object with respect to other is called relative speed.

Suppose two objects are moving with speeds of x km/h and y km/h respectively,

then their relative speed will be;

➢ (x + y) km/h, if both the objects are moving in opposite direction.

➢ (x – y) km/h, if both the objects are moving in the same direction.

Important formulas to remember on SDT topic are as follows;

1. If A travels with speed x km/h for t hours and with speed y km/h for T

hours, then average speed is given by 𝒙𝒕+𝒚𝑻

𝒕+𝑻

2. If a man/ vehicle covers two equal distances with the speed of x km/h

and y km/h respectively, then the average speed of the man/ vehicle for

complete journey will be 𝟐𝒙𝒚

𝒙+𝒚

3. If a man changes his speed to 𝒙

𝒚 of his usual speed and gets late by t min,

then the usual time taken by him 𝒕𝒙

𝒚−𝒙 .

4. When a man travels from A to B with a speed x km/h and reaches t hours

later after the fixed time and when he travels with a speed y km/hr from

A to B, he reaches his destination T hours before the fixed time, then

distance between A and B is 𝒙𝒚(𝒕+𝑻)

𝒚−𝒙km.

5. A person travels from A to B with a speed x km/h and reaches t hours

late. Later he increases his speed by y km/h to cover the same distance

and he still gets late by T hours, then the distance between A and B is

(𝒕 − 𝑻)(𝒙 + 𝒚)𝒙

𝒚 .

6. For Problems based on Trains:

• Time taken by a train x m long in passing a single post or pole or

standing man = Time taken by the train to cover x m.

• Time taken by a train x m long in passing an object of length y m =

Time taken by the train to cover (x + y) m.

• Time taken by a train of length l meter moving at a speed of s m/s

to cross another train of length L moving at a speed of S m/s in

same or opposite direction is 𝒍+𝑳

𝒔±𝑺 .

• If two trains start at the same time from points A and B towards

each other and after crossing each other, they take t and T time in

reaching points B and A respectively, then ratio of their speed is

𝒔

𝑺= √

𝑻

𝒕 .

7. For Problems based on Boats and Streams:

• Still Water: If the speed of water is zero, then water is still water.

• Stream Water: If the water of a river is moving at a certain speed,

then it is called stream water.

• Downstream motion: In water, the direction along the stream is

called downstream.

• Upstream motion: In water, the direction against the stream is

called upstream.

• If the speed of a boat in still water be x km/h and speed of stream

be y km/h, then

a. Speed of boat downstream = (x +y) km/h

b. Speed of boat upstream = (x-y) km/h

• Let the speed of boat in downstream be u km/h and speed of boat

in upstream be v km/h, then (most frequently used shortcut

formula for problems based on Boats and Stream are);

c. Speed of boat in still water = 𝟏

𝟐(𝒖 + 𝒗) km/h

d. Speed of stream (current) = 𝟏

𝟐(𝒖 − 𝒗) km/h

8. For problems based on Races:

• A contest of speed in running, driving, riding, sailing or rowing

over a specified distance is called a race.

• Suppose A and B are two contestants in a race. If A beats B x m

and length of the track is d m. Then the distance travelled by B

when A finishes the race is equal to d – x then,

𝑺𝒑𝒆𝒆𝒅 𝒐𝒇 𝑨

𝑺𝒑𝒆𝒆𝒅 𝒐𝒇 𝑩=

𝒅

𝒅 − 𝒙

• Note:

➢ A gives B a start of x m means when A starts at starting

point, B starts at starting point, B starts x m ahead from

starting point.

➢ A gives B a start of t s means A starts t s after B starts

from the same point.

2. Work and Time

Most of the aptitude questions on work and Time can be solved if you know the basic

correlation between time, work and man-hours which you have learnt in your high

school class.

Shortcuts for frequently asked Time and Work problems:

1. More men can do more work.

2. More work means more time required to do work.

3. More men can do more work in less time.

4. M men can do a piece of work in T hours, then

Total effort or work =MT man hours

Rate of work * Time = Work Done

5. If A can do a piece of work in D days, then A's 1 day's work = 𝟏

𝑫

6. Part of work done by A for, t days =𝒕

𝑫 .

7. If A's 1 day's work = 𝟏

𝑫, then A can finish the work in D days.

𝑴𝑫𝑯

𝑾=Constant

Where,

M = Number of men

D = Number of days

H = Number of hours per day

W = Amount of work

8. If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can

do W2 work in D2 days working H2 hours per day, then 𝑴𝟏𝑫𝟏𝑯𝟏

𝑾𝟏=

𝑴𝟐𝑫𝟐𝑯𝟐

𝑾𝟐

9. If A is x times as good a workman as B, then:

Ratio of work done by A and B = x:1

Ratio of times taken by A and B to finish a work = 1:x

i.e.; A will take 𝟏

𝒙th of the time taken by B to do the same work.

10. If A and B can do a piece of work in x days and y days, respectively. Then, time taken

by A and B together to complete the work is 𝒙𝒚

𝒙+𝒚

11. If A and B can do a piece of work in x days. B and C can do work in y days, C and A

can do same work in z days. Then, they will complete the same work in 𝟐𝒙𝒚𝒛

𝒙𝒚+𝒚𝒛+𝒛𝒙

days by working together.

12. If A and B can complete a work in x days and A alone can finish that work in y days,

then number of days required to complete the work by B is =𝒙𝒚

𝒙−𝒚

13. If two groups 𝑀1, persons of the first group can do 𝑊1 work in 𝐷1 days working 𝑇1

hours in a day and 𝑀2 persons of the second group can do 𝑊2 work in 𝐷2 days

working 𝑇2 hours in a day. If each person of both group has the same efficiency of

work, then 𝑴𝟏𝑫𝟏𝑻𝟏𝑾𝟐 = 𝑴𝟐𝑫𝟐𝑻𝟐𝑾𝟏

14. If m men or n women can do a piece of work in a day’s then x men and y women can

do the same work in 𝟏

𝒙

𝒎𝒂+

𝒚

𝒏𝒂

day.

15. If A can do a work in x days and B can do y% fast than A, then B will complete the

work in 𝟏𝟎𝟎𝒙

𝟏𝟎𝟎+𝒚 days.

16. If A, B and C can do a piece of work in x, y and z days, respectively and they received

RS. K as wages by working together, then

Share of A = 𝑹𝒔.𝒚𝒛

𝒙𝒚+𝒚𝒛+𝒛𝒙× 𝒌

Share of B = 𝑹𝒔.𝒙𝒛

𝒙𝒚+𝒚𝒛+𝒛𝒙× 𝒌

Share of C = 𝑹𝒔.𝒙𝒚

𝒙𝒚+𝒚𝒛+𝒛𝒙× 𝒌

Simple tricks to be followed to solve problems based on Pipes and Cisterns:

1. Time taken to fill tank is considered as positive and noted with (+) sign.

2. Time taken to empty tank is considered as negative noted with (-) sign.

3. If a pipe can fill or empty a tank in x hours, then the part of tank filled or emptied

in 1 hour is 1/x.

4. If pipe can fill or empty 1/x part of a tank in 1 hour, then it can fill or empty the

whole tank in x hours.

5. If a pipe fills a tank in x hours and another pipe fills the same tank in t hours.

Then total part filled by both pipes in 1 hour is 1/x + 1/y.

3. Percentage

Per cent is a fraction whose denominator is 100 and numerator of the fraction is called

the rate per cent. Per cent is denoted by the symbol ‘%’

Shortcuts for frequently asked Percentage problems:

1. For expressing a% as a fraction, we can write 𝒂% =𝒂

𝟏𝟎𝟎.

2. For expressing a fraction 𝒂

𝒃 as a percent we can write

𝒂

𝒃= (

𝒂

𝒃× 𝟏𝟎𝟎) %

3. To find how much percent one quantity is of another quantity;

Required percentage = 𝑻𝒉𝒆 𝒒𝒖𝒂𝒏𝒕𝒊𝒕𝒚 𝒕𝒐 𝒃𝒆 𝒆𝒙𝒑𝒓𝒆𝒔𝒔𝒆𝒅 𝒊𝒏 𝒑𝒆𝒓 𝒄𝒆𝒏𝒕

𝟐𝒏𝒅 𝒒𝒖𝒂𝒏𝒕𝒊𝒕𝒚× 𝟏𝟎𝟎%

4. Percentage increase or decrease in a quantity when it increases or decreases by

some value.

Percentage =𝑰𝒏𝒄𝒓𝒆𝒂𝒔𝒆 𝒐𝒓 𝒅𝒆𝒄𝒓𝒆𝒂𝒔𝒆 𝒊𝒏 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆

𝑰𝒏𝒊𝒕𝒊𝒂𝒍 𝒗𝒂𝒍𝒖𝒆× 𝟏𝟎𝟎%

5. If ‘A’ is x% more than ‘B’, then B would be [𝒙

𝟏𝟎𝟎+𝒙× 𝟏𝟎𝟎] % less than ‘A’.

6. If ‘A’ is x% less than ‘B’, then B would be [𝒙

𝟏𝟎𝟎−𝒙× 𝟏𝟎𝟎] % more than ‘A’.

7. If the price of commodity is increased or decreased by x%, then decrease or

increase in consumption, so as not to increase or decrease the expenditure is

(𝒙

𝟏𝟎𝟎±𝒙× 𝟏𝟎𝟎) %.

8. If the value of an object is first changed (increased or decreased) by x% and then

changed (increased or decreased) by y%, then

Net effect = (±𝒙 ± 𝒚 +(±𝒙)(±𝒚)

𝟏𝟎𝟎) %

9. If the population of a town is P and it increase or decrease at the rate of R% per

annum, then

Population after n year = 𝑷 (𝟏 ±𝑹

𝟏𝟎𝟎)

𝒏

Population, n year ago =𝑷

(𝟏±𝑹

𝟏𝟎𝟎)

𝒏

10. If present population of a city is P and there is an increment or decrement of

𝑅1%, 𝑅2% and 𝑅3% in first, second and third year respectively, then

Population of city after 3 years = 𝑷 (𝟏 ±𝑹𝟏

𝟏𝟎𝟎) (𝟏 ±

𝑹𝟐

𝟏𝟎𝟎) (𝟏 ±

𝑹𝟑

𝟏𝟎𝟎)

4. Average

Average refers to the sum of observations divided by number of observations. Also

called as mean average.

Shortcuts for frequently asked Average problems:

1. Average =𝑺𝒖𝒎 𝒐𝒇 𝒅𝒂𝒕𝒂 𝒗𝒂𝒍𝒖𝒆𝒔

𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒅𝒂𝒕𝒂 𝒗𝒂𝒍𝒖𝒆𝒔 𝒂𝒅𝒅𝒆𝒅 𝒂𝒃𝒐𝒗𝒆 𝒊𝒏 𝒏𝒖𝒎𝒆𝒓𝒂𝒕𝒐𝒓

2. Average of first n natural numbers is 𝒏+𝟏

𝟐.

3. Average of squares of first ‘n’ natural numbers is (𝒏+𝟏)(𝟐𝒏+𝟏)

𝟔

4. Average of cubes of first ‘n’ natural numbers is 𝒏(𝒏+𝟏)𝟐

𝟒

5. Average of first n even natural numbers is (𝒏 + 𝟏)

6. Average of first n odd numbers is n.

5. Simple & Compound Interest

Interest is the cost of borrowing money, where the borrower pays a fee to the lender for using the latter's money. The interest, typically expressed as a percentage, can be either simple or compounded. Simple interest is based on the principal amount of a loan or deposit, while Compound interest is based on the principal amount and the interest that accumulates on it in every period. Since simple interest is calculated only on the principal amount of a loan or deposit, it's easier to determine than compound interest. Shortcuts for frequently asked Simple and Compound Interest problems:

1. Simple Interest=𝑷𝑹𝒏

𝟏𝟎𝟎, where P is Principal, R is rate of interest and n is duration.

2. If the sum of money becomes n times in ‘T’ years at simple interest, then rate of

interest will be, 𝑹 = (𝟏𝟎𝟎(𝒏−𝟏)

𝑻) %

3. If a certain Principal Amounts to ₹ A in t years and to B in T years, then the sum(P) is

given by ₹ (𝑩𝒕−𝑨𝑻

𝒕−𝑻) % and the rate of interest(R) is given by (

𝟏𝟎𝟎(𝑩−𝑨)

𝑨𝑻−𝑩𝒕) %

4. At the same rate of simple interest, if a sum of money becomes 𝑛1 times of itself in

𝑡1 years and 𝑛2 times in 𝑡2 years, then 𝒕𝟐 =(𝒏𝟐−𝟏)

(𝒏𝟏−𝟏)𝒕𝟏 years.

5. When interest is compounded annually, then

Amount= 𝑷 (𝟏 +𝑹

𝟏𝟎𝟎)

𝒏 𝒂𝒏𝒅 𝒄𝒐𝒎𝒑𝒐𝒖𝒏𝒅 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕 CI= 𝑨 − 𝑷

6. When interest is compounded half-yearly, then 𝑨 = 𝑷 (𝟏 +𝒓

𝟐𝟎𝟎)

𝟐𝒏

7. When interest is compounded quarterly, then 𝑨 = 𝑷 (𝟏 +𝑹

𝟒𝟎𝟎)

𝟒𝒏

8. When interest is compounded annually but time is given fraction say (t 𝒂

𝒃 year),

then 𝑨 = 𝑷 (𝟏 +𝑹

𝟏𝟎𝟎)

𝒕× (

𝟏+(𝒂

𝒃)𝑹

𝟏𝟎𝟎)

9. When rate of interest for 𝑛1, 𝑛2 and 𝑛3 years are 𝑅1, 𝑅2and 𝑅3 respectively, then

𝑨𝒎𝒐𝒖𝒏𝒕 = 𝑷 (𝟏 +𝑹𝟏

𝟏𝟎𝟎)

𝒏𝟏 (𝟏 +

𝑹𝟐

𝟏𝟎𝟎)

𝒏𝟐 (𝟏 +

𝑹𝟑

𝟏𝟎𝟎)

𝒏𝟑

10. The difference D between simple and compound interest accrued on ₹ P at the rate

of interest of r% is given by

For 2 year, 𝑫 =𝑷𝑹𝟐

𝟏𝟎𝟎𝟐

For, 3 years, 𝑫 =𝑷𝑹𝟐(𝟑𝟎𝟎+𝒓)

𝟏𝟎𝟎𝟑

11. If a certain sum at compound interest becomes 𝐴1, in n years and 𝐴2 in (n + 1)

years, then

Rate of compound interest =(𝑨𝟐−𝑨𝟏)

𝑨𝟏× 𝟏𝟎𝟎%

Sum= 𝑨𝟏 (𝑨𝟏

𝑨𝟐)

𝒏

6. Ratio and Proportion

If a and b are two quantities of same kind, then the fraction a/b is called the ratio a to b

and we write it as a: b. Here a is called antecedent and b is called the consequent.

Shortcuts for frequently asked Ratio and Proportion problems:

Compound Ratio: When two or more ratios are multiplied together, they are said to be

compound ratio.

Duplicate Ratio: when a ratio is compounded with itself, the resulting ratio is called the

duplicate ratio.

Triplicate Ratio: If a ratio is compounded three times with itself, then resulting ratio is

called triplicate ratio.

Subduplicate Ratio: If two numbers are in ratio, then the ratio of their square roots is

called Subduplicate ratio.

Subtriplicate Ratio: If two numbers are in ratio, then the ratio of their cube roots is

called Subtriplicate ratio.

Reciprocal Ratio: If a: b is a ratio, then 1/a: 1/b is its reciprocal ratio.

Proportion: The equality of two ratios is called proportion. ‘::’ is the sign of proportion.

Continued Proportion: The non-zero quantities of same kind, a, b, c, d, e, f, … are said to

be continued proportion, if 𝒂

𝒃=

𝒃

𝒄=

𝒄

𝒅=

𝒆

𝒇= ⋯

Mean Proportional: If a, b and c are in continued proportion, then b is called the mean

proportional of a and c.

Third Proportional: If 𝒂: 𝒃 ∷ 𝒃: 𝒄, then c is called the third proportional to a and b.

Fourth Proportional: If four numbers or quantities a, b, c and d are in proportion, then d

is known as fourth proportional.

Mixture: If two or more quantities are mixed in a certain ratio, then the product is called

Mixture.

If two quantities are mixed in the ratio 𝒏𝟏: 𝒏𝟐, then

𝒏𝟏

𝒏𝟐=

𝑪𝒉𝒆𝒂𝒑𝒆𝒓 𝑸𝒖𝒂𝒏𝒕𝒊𝒕𝒚

𝑫𝒆𝒂𝒓𝒆𝒓 𝑸𝒖𝒂𝒏𝒕𝒊𝒕𝒚=

𝒑𝟐 − 𝒑𝒎

𝒑𝒎 − 𝒑𝟏

7. Profit & Loss

Cost Price: The price, at which an article is purchased, is called its cost price, abbreviated as

C.P.

Selling Price: The, price, at which an article is sold is called its selling price, abbreviated

as S.P.

Profit or Gain: If S.P. is greater than C.P. the seller is said to have a Profit or Gain.

Loss: If S.P. is less than C.P. then the seller is said to have incurred a Loss.

Shortcuts for frequently asked Profit and Loss problems:

1. Gain = (S.P.) - (C.P.)

2. Loss = (C.P.) - (S.P.)

3. Gain Percentage: (Gain %)= (𝑮𝒂𝒊𝒏×𝟏𝟎𝟎

𝑪𝑷)

4. Loss percentage: (Loss%)= (𝑳𝒐𝒔𝒔×𝟏𝟎𝟎

𝑪𝑷)

5. Selling Price: (S.P.) = (𝟏𝟎𝟎−𝑳𝒐𝒔𝒔%

𝟏𝟎𝟎) × 𝑪𝑷

6. Selling Price: (S.P.) = (𝟏𝟎𝟎+𝑮𝒂𝒊𝒏%

𝟏𝟎𝟎) × 𝑪𝑷

7. Cost Price: (C.P.) = (𝟏𝟎𝟎

𝟏𝟎𝟎+𝑮𝒂𝒊𝒏%) × 𝑺𝑷

8. Cost Price: (C.P.) = (𝟏𝟎𝟎

𝟏𝟎𝟎−𝑳𝒐𝒔𝒔%) × 𝑺𝑷

9. If an article is sold at a gain of say 25%, then S.P. = 125% of C.P.

10. If an article is sold at a loss of say, 25% then S.P. = 75% of C.P.

11. When a person sells two similar items, one at a gain of say x%, and the other at a loss

of x%, then the seller always incurs a loss given by:

𝑳𝒐𝒔𝒔% = (𝑪𝒐𝒎𝒎𝒐𝒏 𝑳𝒐𝒔𝒔 𝒂𝒏𝒅 𝑮𝒂𝒊𝒏 %

𝟏𝟎)

𝟐

= (𝒙

𝟏𝟎)

𝟐

12. If a trader professes to sell his goods at cost price, but uses false weights, then

𝑮𝒂𝒊𝒏% = (𝑬𝒓𝒓𝒐𝒓

𝑻𝒓𝒖𝒆 𝒗𝒂𝒍𝒖𝒆 − 𝑬𝒓𝒓𝒐𝒓× 𝟏𝟎𝟎) %

8. Decimal Fractions/Simplification

A decimal fraction is a fraction in which denominator is an integer power of ten. (The

term decimals are commonly used to refer decimal fractions). Generally, a decimal

fraction is expressed using decimal notation and its denominator is not mentioned

explicitly.

Simplification: Rule of ‘BODMAS’: This BODMAS rule depicts the correct sequence in which the operations are to be executed, so as to find out the value of given expression. Full form of BODMAS is B – Bracket, O – of, D – Division, M – Multiplication, A – Addition and S – Subtraction. Thus, while solving or simplifying a problem, first remove all brackets, strictly in the order (), {} and ||. After removing the brackets, we will use the following operations strictly in the following order: (i) of (ii) Division (iii) Multiplication (iv) Addition (v) Subtraction.

Some Basic Formulas used to solve problems based on fractions and Simplification

1. (a + b) (a – b) = (a2 – b2) 2. (a + b)2 = (a2 + b2 + 2ab) 3. (a – b)2 = (a2 + b2 – 2ab) 4. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) 5. (a3 + b3) = (a + b) (a3 – ab + b2) 6. (a3 – b3) = (a – b) (a2 + ab + b2)

7. (a3 + b3 + c3 – 3abc) = (a + b + c) (a2 + b2 + c2 – ab – bc – ac) 8. When a + b + c = 0, then a3 + b3 + c3 = 3abc.

https://play.google.com/store/apps/details?id=com.ssbcrackexams.learn